
School of Mathematics and Statistics
Piotr Hajac
Mathematisches Institut, Universitaet Muenchen, Germany
Noncommutative geometry of algebraic bundles
Friday 10th August, 121pm,
Carslaw 375.
CoalgebraGalois extensions of noncommutative algebras are algebraic
analogues of principal bundles. To any such an extension one can
associate
modules much as vector bundles are associated to principal bundles. We
show
the equivalence of the relative projectivity of coaugmented
coalgebraGalois extensions and existence of strong connections. Then we
prove that modules associated to such extensions via finite dimensional
corepresentations are finetely generated projective, and thus fit the
formalism of the ChernConnes pairing between Ktheory and cyclic
cohomology. As an example, we use the ChernConnes pairing to define,
and
the Noncommutative Index Theorem to compute, the Chern numbers of
algebraic
line bundles associated to the qdeformed Hopf fibration.
